Question

Consider the following expression and the simplified expression. Expression Simplified Expression 3x^2+5y +3 +4y^2+6 9x^2-7^2+9 Which terms could be in the boxes to make the expressions equivalent?

Answer 1

Answer:

The correct answer option is $+6x^2$ and $-10y^2$.

Step-by-step explanation:

We are given the following incomplete expression:

$3 x^2 + 5 y^2$ __ $+ 3$ __ $+ 4 y^2 + 6$

and then there is its simplified expression as shown below:

$9 x^2 - y^2 + 9$

We are to determine whether which terms could be in the boxes to make the expressions equivalent.

$+6x^2$ and $-10y^2$ are the two terms which justify the given expression:

$3 x^2 + 5 y^2 +6x^2 + 3 -10y^2 + 4 y^2 + 6 = 9 x^2 - y^2 + 9$

Answer 2

Answer:

$+6x^2$ and $-10y^2$

Step-by-step explanation:

Let's go one term at a time from the right side and match it with the left side.

• On the right hand side, we have $9x^2$. On the left side we have $3x^2$. So we would need a $6x^2$. Hence we can eliminate option C and D immediately.

• On the right hand side, we have  $-y^2$. On the left side we have  $5y^2$ and $4y^2$, which is equal to $9y^2$. So we would need to subtract $10y^2$ to make right hand side into  $-y^2$.

Clearly Option B is right.